Original
A power line needs to be run from a power station located on the
beach to an offshore facility.
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It costs {{CMD_131}}50/ft. to run a power line along the land, and {{CMD_132}}130/ft. to
run a power line under water. How much of the power line should be run
along the land to minimize the overall cost? What is the minimal cost?
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There are two immediate solutions that we could consider, each of
which we will reject through ``common sense.'' First, we could
minimize the distance by directly connecting the two locations with a
straight line. However, this requires that all the wire be laid
underwater, the most costly option. Second, we could minimize the
underwater length by running a wire all 5000 ft. along the beach,
directly across from the offshore facility.